Method and apparatus for locating a buried metallic object

ABSTRACT

A unique time-domain electromagnetic system and data processing technique which, using low frequency electromagnetic fields, can localize, in three-dimensions, the position of buried metallic objects is disclosed. The measurement system uses time-domain electromagnetic techniques on a scanning frame similar to a X-Y plotter. The system collects magnetic data over a large area above the buried object. The spatial information of the field detected on the ground is then processed with an unique ‘nearfield holographic’ data processing method to reconstruct the field image of the buried object.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This is a divisional of prior filed copending application Ser.No. 08/824,644, filed Mar. 24, 1997 which claims the benefit of priorfiled copending U.S. provisional application serial No. 60/014,151,filed Mar. 25, 1996.

STATEMENT OF GOVERNMENTAL INTEREST

[0002] This invention was made with Government support under ContractNo. N00039-94-C-0002 awarded by the Department of the Navy. TheGovernment has certain rights in the invention.

BACKGROUND OF THE INVENTION

[0003] Detection of underground objects has long been a very activeresearch subject because of its important applications in minedetection, geological exploration, forensic investigation, treasurehunting, etc. Recent emphasis on environmental clean-up and remediation,has increased interest in this area. In converting abandoned militarybases to civil use and in cleaning old battle fields, objects left inthe ground, such as shells, unexploded ordnance (UXO), etc., need to bedetected and removed.

[0004] Most of the techniques and systems currently available for thedetection of underground objects are of the type which search thedesignated area and indicate the possible existence of some undergroundobjects. They lack the capability to precisely locate and characterizethe objects.

[0005] The difficulty in characterizing underground objects withelectromagnetic (EM) methods stems from the ground medium surroundingthe objects. Unlike air which is transparent and almost lossless for EMwave propagation, the ground is conductive and generally inhomogeneouscausing an increase in signal dissipation and localization errors. Sincedissipation increases with the EM frequency, it limits the use of the EMenergy to low frequency bands when depth penetration beyond severalmeters is desired.

[0006] In air, the electromagnetic field satisfies the Helmholtz waveequation and operates in a propagation mode at distances between thesource and the receiver much greater than a free space wavelength. Theamplitude of the fields either remains constant or changes relativelyslowly, but the phase changes rapidly with distance. From the phasedelay of an electromagnetic field reflected from a target one can tellthe range between the target and the observer. The directivity, orfocused direction, along which the antenna transmits and receives theelectromagnetic field gives the direction of the target. The rangecombined with the direction indicates the location of the target.

[0007] In contrast, in the ground, at measurement ranges much less thana wavelength, the electromagnetic field basically satisfies a diffusiontype equation in the low frequency limit, rather than the usual waveequation as in the air. For distances much less than a wavelength, thephase delay, related to the spatial variation of the waves (i.e.,e^(i2πx/λ)), is too small to be used to measure the object's range andshape or to resolve multiple objects. In addition, the small size of thetransmitter and receiver aperture relative to a wavelength does notprovide a capability for measuring direction to the buried object.

[0008] Because of the potential danger involved in the remediation ofabandoned military bases and old battlefields, not just the detection ofthe underground objects is required, but a more precise characterizationwhich includes location, orientation, size, shape, and materialcomposition is desirable. New technological systems which can satisfythese requirements are in urgent demand.

SUMMARY OF THE INVENTION

[0009] The invention is a method of localizing highly conducting, (e.g.,metallic) buried objects by measuring their field distribution on orabove the surface and then reconstructing the field as a function ofdepth in the ground utilizing a nearfield holography algorithm. Thethree dimensional locations of the objects are determined from thereconstructed field images of the objects. Also disclosed is atime-domain electromagnetic sensor system that collects the data used bythe nearfield holographic technique of the invention.

[0010] The conventional ranging method is based on the observation of aphase change, i.e., the temporal change, of the field at a fixed stationin space. For underground objects located at a distance of a smallfraction of a wavelength, i.e., located in the nearfield, the temporalchange of the field is negligible. However, in the diffusion region themagnitude of the field is very sensitive to the distance from theobject. Since the field decays approximately inversely as the thirdpower of the distance, a small change in distance leads to a significantchange in the field magnitude. Based on this fact, instead of observingthe temporal field change at a fixed point in space, more accurateinformation about underground objects can be obtained by examining thespatial change of the field in a plane above the ground.

[0011] In its simplest form, the nearfield holographic technique is acombination of an EM measurement procedure and a method for treating theresulting EM data. The area where the object is buried is illuminatedwith an active transient time-domain EM source located on or above theground and scanned over an mxn grid on the surface. The field radiatedfrom the source penetrates into the ground and induces eddy currentsinside the object. These eddy currents act as a secondary source whichre-radiates EM fields. The re-radiated EM fields from the object, or thetime-rate-of-change of the secondary magnetic fields, are then measuredat each of the points on the mxn grid in a horizontal plane at thesurface of the ground in the vicinity of the buried object.

[0012] For a sensor/receiver coil operating in a time domain mode, thereceived signal at each grid point is Fourier transformed to thefrequency domain, so that the secondary magnetic fields re-radiated fromthe object are obtained as a function of frequency. The characteristicfrequency from the resulting frequency domain response, or themeasurement frequency for a sensor/receiver coil operating in thefrequency domain, is used as the image reconstruction frequency.

[0013] The magnetic field, after being transformed into the frequencydomain, is a complex function having both magnitude and phase. At aparticular frequency, the magnetic fields at the individual grid pointsin the detection plane form a spatial distribution of the measuredmagnetic field in that plane. The spatial variation of the magneticfield depends on the characteristics of the buried object and thedistance from the object. This spatial distribution of the magneticfield at the detection plane is used to reconstruct the magnetic fielddistribution in the horizontal plane at various depths in the ground byspatial Fourier transforms and a backward propagation algorithm. It isfirst Fourier transformed in two dimensions to form the spatialfrequency spectrum. This spectrum is multiplied by a propagationfunction determined from the Helmholtz equation for a desired depth, d.The result is inverse Fourier transformed in two dimensions to producethe reconstructed image at depth, d.

[0014] The above process is repeated for a range of depths, d, thatbracket the expected depths of the buried objects. The resulting imagesin the back propagated planes, i.e., the reconstructed magnetic fielddistributions, are then examined to resolve closely spaced objects andto determine the depth and the location in the horizontal plane. Thedepth of the object is the point where the image is the smallest, orfocused, since the re-radiated fields expand in all directions from thelocation of the object.

[0015] Thus, the invention meets the goal of locating and resolvinghighly conducting buried objects such as UXO and mines, which are smallin size and shallow compared to general geological structures, that areburied in the nearfield, i.e., at depths and separated by distances muchless than a wavelength.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016]FIG. 1 illustrates in schematic form the nearfield electromagneticholographic method of the invention.

[0017]FIG. 2 illustrates the arrangement of two ideal dipole sourceslocated in a conductive medium.

[0018]FIG. 3 is a plot of the resultant magnetic field of the two idealdipole sources at the interface.

[0019]FIG. 4 displays a field image of the two ideal dipole sourcesmeasured at the interface and the reconstructed field images at variousdepths down to 1.1 meters.

[0020]FIG. 5 is a plot of a resultant magnetic field at the interfaceresulted from the two band limited point sources located in a conductivemedium.

[0021]FIG. 6 displays reconstructed field images of the two bandlimitedpoint sources at depths from 0.7 m to 1.1 m.

[0022]FIG. 7 is a simplified diagram of the time-domain electromagneticmeasurement technique.

[0023]FIG. 8 illustrates a time-domain electromagnetic system andscanning frame.

[0024]FIG. 9 illustrates the claw and control arm portion of theclaw/piston system of the invention attached to a sliding support plate.

[0025]FIG. 10 illustrates the claw/piston system of the invention.

[0026]FIG. 11, consisting of FIGS. 11(a), 11(b), and 11(c), illustratesthe operation of the claw/piston system.

[0027]FIG. 12 is a block diagram of the time-domain electromagneticsystem of the invention.

[0028]FIG. 13 is a diagram of the individual receiver amplifiers andgeneral transmitter electronics of the invention.

[0029]FIG. 14, comprising FIGS. 14(a), 14(b) and 14(c), illustratesconfigurations of the test objects: 14(a) two steel pipes suspendedabove the ground; 14(b) two steel pipes buried in the ground; and 14(c)a cannon ball buried in the ground.

[0030]FIG. 15 displays a field image of two suspended steel pipesmeasured at the surface and the reconstructed field images at variousheights up to 1.1 meters.

[0031]FIG. 16 displays a field image of two buried steel pipes measuredat the surface and the reconstructed field images at various depths downto 1.1 meters.

[0032]FIG. 17 are plots of the reconstructed magnetic fielddistributions of the two buried steel pipes at four depths.

[0033]FIG. 18 displays a field image of a buried cannon ball measured atthe surface and the reconstructed field images at various depths down to1.1 meters.

[0034]FIG. 19 are plots of the reconstructed magnetic fielddistributions of the two aluminum disks at four depths.

DETAILED DESCRIPTION OF THE INVENTION

[0035] The invention's goal is to identify the location of undergroundobjects based on the image of a reconstructed field distribution in theground from the measured field above or on the ground. The primaryelectromagnetic field originating from an illuminating source withlimited dimension will spread out in space and impinge on an object.Similarly, viewed in a vertical set of horizontal planes, the spatialsize of the secondary field, induced from an object, increases in eachhorizontal plane as a function of the vertical distance from the object.

[0036] If the images of the induced field distribution in a series ofhorizontal planes are displayed along the vertical direction startingfrom a detection plane above the object downward to a plane deeper thanthe object, one will observe the image pattern varying gradually from alarge spot to a small one, and then becoming a large one again. Thechange of the image pattern corresponds to the change of the spatialspreading of the field. The smallest, or the most focused, image patternshould occur in the plane where the object is located because the objectis the source of the induced field. An estimate of the depth of theobject is therefore obtained and the image of the field distribution inthat plane will give the horizontal location of the object.

[0037] From the field images displayed in horizontal or level planes,one can also resolve closely spaced multiple objects. The field detectedat the surface is the resultant field of the fields induced in eachobject if there is more than one object involved. The complete surfacemeasured field may not indicate the number of objects if the spread ofthe individual object fields overlap each other because of their closeproximity to each other. When the measured field is reconstructed at theobject level plane, each individual induced field becomes confined tothe object, and hence the individual objects become separatelyidentifiable.

[0038] To implement the reconstruction of the field in the ground fromthe field measured on the surface, a field reconstruction method hasbeen developed, which is called nearfield electromagnetic holography asillustrated in FIG. 1.

[0039] To describe the field reconstruction algorithm, first considerthe case of localizing a source in free space. We assume that thecomplex function f₀(x_(o),y_(o)) represents one of the components of theelectromagnetic field of the source measured at plane z=0 with thez-axis pointing upwards, and that the source is located below themeasurement plane at z=−d. The distribution of the field at thedetection plane may be decomposed into a series of plane waves through aFourier transform $\begin{matrix}{{F_{0}\left( {k_{x},k_{y}} \right)} = {\int{\int_{- \infty}^{+ \infty}{{f_{0}\left( {x_{0},y_{0}} \right)}^{{- }\quad {({{x_{0}k_{x}} + {y_{0}k_{y}}})}}{x_{0}}{y_{0}}}}}} & (1)\end{matrix}$

[0040] where k_(x) and k_(y) are the spatial frequencies of theelementary plane waves. The e^(−iωt) time oscillation is assumed for thefield throughout. On the other hand, the distribution of the field atthe source plane (f_(z)), or at the other level planes, may be obtainedby a superposition of the plane waves utilizing an inverse Fouriertransform, $\begin{matrix}{{f_{z}\left( {x,y,z} \right)} = {\frac{1}{\left( {2\pi} \right)^{2}}{\int{\int_{- \infty}^{+ \infty}{{F_{z}\left( {k_{x},k_{y},z} \right)}^{\quad {({{k_{x}x} + {k_{y}y}})}}{k_{x}}{k_{y}}}}}}} & (2)\end{matrix}$

[0041] The spectrum F_(z)(k_(x),k_(y),z) namely, the distribution of theplane waves in k space at a level plane, should be related to the one atthe detection plane. In the forward process, the plane waves arepropagated from the source plane to the detection plane. In the inverseprocess, we may let the plane waves propagate backward from thedetection plane to a level plane. Therefore the spectral function at alevel plane may be expressed as the spectrum at the detection planemultiplied by a propagation function

F _(z)(k _(x) ,k _(y) ,z)=F ₀(k _(x) ,k _(y))P(k _(x) ,k _(y) ,z)   (3)

[0042] The propagator P(k_(x),k_(y),z) may be determined from theHelmholtz equation which the electromagnetic field obeys in thehomogeneous medium. Consider the field at a plane with arbitrary z,$\begin{matrix}{{f_{z}\left( {x,y,z} \right)} = {\frac{1}{\left( {2\pi} \right)^{2}}{\int{\int_{- \infty}^{+ \infty}{{F_{0}\left( {k_{x},k_{y}} \right)}{P\left( {k_{x},k_{y},z} \right)}^{\quad {({{k_{x}x} + {k_{y}y}})}}{k_{x}}{k_{y}}}}}}} & (4)\end{matrix}$

[0043] which upon substitution into the Helmholtz equation$\begin{matrix}{{{{\nabla^{2}{f_{z}\left( {x,y,z} \right)}} + {k_{0}^{2}{f_{z}\left( {x,y,z} \right)}}} = 0},} & (5)\end{matrix}$

[0044] leads to the following differential equation for the propagator:$\begin{matrix}{{\frac{\partial^{2}P}{\partial z^{2}} + {\left( {k_{0}^{2} - k_{x}^{2} - k_{y}^{2}} \right)P}} = 0} & (6)\end{matrix}$

[0045] where k₀ is the wave number of the electromagnetic field in themedium. For this introductory free space illustration $\begin{matrix}{k_{o} = \frac{\omega}{C}} & (7)\end{matrix}$

[0046] where ω is the angular frequency of the source field and c is thelight speed in air.

[0047] From this equation and the initial condition at the detectionplane the propagator is found to be $\begin{matrix}{{P\left( {k_{x},k_{y},z} \right)} = {\exp \left( {{iz}\sqrt{k_{0}^{2} - k_{x}^{2} - k_{y}^{2}}} \right)}} & (8)\end{matrix}$

[0048] The propagator P(k_(x),k_(y),z) describes how each of theelementary plane waves propagates backward in the vertical direction. Itis observed from the expression for the propagator given by Eq. (8) thatnot all of the plane waves propagate in the same way. There are twokinds of waves depending on whether the wave number (k_(x) ²+k_(y) ²) isgreater or less than the wave number of the illuminator source field k₀². When k_(x) ²+k_(y) ²<k₀ ², the square root in Eq. (8) is real, sothat the propagator only modifies the phase of the wave. The waves thatsatisfy this condition are called the propagating waves, theiramplitudes remain unchanged and only their phases change whenpropagating. However when k_(x) ²+k_(y) ²>k₀ ², the square root in Eq.(8) is an imaginary number, and the propagator becomes an exponentialfunction of the vertical distance. In the forward process, theamplitudes of these waves decrease exponentially as they propagate, andthe waves in this case are called evanescent waves.

[0049] In conventional holography, the evanescent waves are normallyneglected in image reconstruction. Since the hologram is generallyrecorded several wavelengths away from the source, the evanescent wavesare small and undetectable. However, in the nearfield case, theevanescent waves can play an important role for improving the resolutionof the reconstructed field. It is the evanescent waves that can help theresolution in the nearfield, low frequency case yielding results betterthan conventional methods.

[0050] The resolution usually refers to the minimum distance between twopoints in space for which their wave field can be distinguished. Hence,the resolution R is related to the highest spatial frequency of thefield as $\begin{matrix}{R = \frac{\pi}{k_{\max}}} & (9)\end{matrix}$

[0051] The maximum spatial frequency in conventional holography is thewave number of the applied source field, i.e., k_(max)=k=2π/λ, so thatthe best resolution is R=λ/2. This is the so-called Rayleigh's criterionindicating that resolution is wavelength-limited. For the problem ofdetecting objects buried in the ground, the wavelength of the appliedelectromagnetic field is typically hundreds of meters in the earth. Theresolution, according to Rayleigh's criterion, will be poor ifconventional holography technique is applied.

[0052] Practically, the distribution of the field radiated from buriedobjects is measured at a distance which is a small fraction of awavelength of the applied electromagnetic field. In this near-fieldrange, some of the evanescent waves are detectable. It thus becomes agreat advantage to utilize the evanescent waves in the reconstruction ofthe field image. The maximum spatial frequency of the field can be muchgreater than the wave number of the applied EM source, and theresolution can be significantly improved. As a result, the resolution isnot limited by the wavelength but depends on the degree to which theevanescent waves can be actually measured.

[0053] To illustrate the above, metallic objects are buried in theground and are assumed to be detected by applying a low frequencyelectromagnetic source, usually an electrical current coil, placed at orabove the ground. The field radiated from the source penetrates into theground and induces eddy currents inside the buried objects. These eddycurrents act as a secondary source re-radiating electromagnetic fields.The fields are then detected by detectors located at or above the groundsurface. The field generated by the source is called the primary field,or the source field, and the field re-radiated from the objects iscalled the secondary field, or the object field. It is the object fieldthat is measured and used to reconstruct the field images.

[0054] Since the source, detector and objects are in different mediathere are multiple reflections at the interface. As described below, theeffects of the direct and interface reflected fields from the source aredealt with by using a transient time-domain sensor system. With thiskind of system, the important secondary field from the object ismeasured during the time interval when the source is turned off.

[0055] For the purpose of reconstruction of the object field in theground, we need only to be concerned with the object field measured atthe surface. Although an accurate object field can not be reconstructedbeneath the surface without knowing the reflected field from thesurface, an approximate solution may be obtained by ignoring thereflected field.

[0056] The purpose of reconstructing the object field at level planeshere is to determine the depth of the object. It is based on theprinciple that the back-propagated object field will converge at theobject's true location. The approximate solution of the object field canstill serve this purpose because the transmitted fields are the mainpart of the outgoing field generated by the object, and they should alsoconverge at, or substantially close to, the object location.

[0057] As we see from Eq. (8), the wave number of the source field inthe medium is needed for the calculation of the propagator. At lowfrequencies, by neglecting displacement currents, the wave number k_(o)in the earth can be approximated as

k_(o)={square root}iωμσ  (10)

[0058] where ω is the angular frequency of the source field, and μ and σare the magnetic permeability and electrical conductivity of the earth,respectively. In most circumstances, the magnetic permeability of theearth is the same as the value in free space. The conductivity of theearth is generally a function of position, but it can be approximatedwith an average value. The propagator is not very sensitive to theinhomogeneity of the conductivity since the values of k_(x) and k_(y) inthe propagator expression are much greater than the wave number in mostcases. When the measurement is not on the earth's surface but on a planein the air, the field is first downward continued to the earth's surfaceusing the wavenumber in the air, Eq. (7), and then downward continuedinto the earth using the wavenumber in the earth given by Eq. (10).

[0059] The conductivity of the earth lies in the range 0.001 S/m (fordry sandy soil) to 0.01 S/m (for marshy soil), while the conductivity ofa metallic object is typically about 10⁶ S/m, which results in a largeconductivity contrast between the object and its surrounding medium. Atlow frequencies, the secondary magnetic field usually dominates thesecondary electric field, and only the magnetic field is measured. inmost cases. Eddy currents will also be induced in the earth itself, butthe field associated with the earth eddy currents is negligible comparedwith the field generated by eddy currents from the highly conductingobject.

[0060] Numerical simulations to demonstrate and verify the localizationmethod will now be considered. The first simulation is to locate twoobjects modeled by unit vertical magnetic dipoles. They are separated bya half meter and placed in a conductive half space one meter below theinterface between the air and the conductive medium, as shown in FIG. 2.The conductivity of the medium surrounding the dipoles is assumed to be0.01 S/m, and the dipoles oscillate at a frequency of 1000 Hz. Themagnetic field radiated from the dipoles is to be measured at theinterface with a horizontally placed coil having its axis in thevertical direction. Therefore, only the z-component of the magneticfield is detected.

[0061] First, the magnetic field of the dipole sources at the interface(measurement plane) produced by the dipole objects needs to begenerated. The general formulas for the electromagnetic field generatedby a magnetic dipole in a conductive half space are known. The integralform of the magnetic field in the low frequency approximation is usedhere. With the dipole source geometry and coordinate system defined inFIG. 2, the vertical magnetic field at the interface due to two unitvertical magnetic dipoles (both pointed in the positive z-direction)buried in a half-conductive medium and located at (-x_(o,)0,-d) and(x_(o,)0,-d) are obtained as $\begin{matrix}\begin{matrix}{H = \quad {\frac{1}{2\pi}{\int_{0}^{\infty}{\frac{u^{3}}{u + \gamma}{^{{- \gamma}\quad d}\left\lbrack {{J_{0}\left( {u\sqrt{\left( {x + x_{0}} \right)^{2} + y^{2}}} \right)} +} \right.}}}}} \\{\left. \quad {J_{0}\left( {u\sqrt{\left( {x - x_{0}} \right)^{2} + y^{2}}} \right)} \right\rbrack {u}}\end{matrix} & (11)\end{matrix}$

[0062] where

γ={square root}u ² −i2πfμ ₀σ

μ₀=4π×10⁻⁷ H/m

σ=0.01 S/m

f=1000 Hz

d=1 m

x₀=0.25 m   (12)

[0063] and J₀ is the Bessel function of the first kind of order zero.

[0064] As shown in FIG. 2, the interface coincides with the plane z=0.The field is assumed to be measured on a grid of points with spacing of0.25 m in both the x and y directions. The magnetic field detected atthe surface is calculated using Eqs. (11-12), and its magnitude,normalized with its maximum value unity, is plotted in FIG. 3. Themeasurement window here covers from −4 meters to 3.75 meters in both thex and y dimensions. As shown in FIG. 3, the magnetic field at theinterface generated by the dipole sources has a maximum at the centerpoint (0,0). The single peaked distribution of the field looks as if thefield was generated by a single source located directly beneath thecenter point and gives no indication that the field was generated by twoseparate sources.

[0065] Using the field reconstruction algorithm of the invention, thefield at level planes of various depths based on the field distributionat the interface was reconstructed. The field amplitude in all of thereconstructed field images for the simulation examples and later for thetested real objects has been normalized by its peak value. FIG. 4displays the field images at level planes arranged in the order ofincreasing depth from the surface down to 1 meter deep. Beyond thisdepth the field continues to spread.

[0066] The image at a level plane depicts the spatial distribution ofthe field in that plane. The sequence of images shown in FIG. 4,manifests the process of change in the field distribution along thevertical direction. By observing the image sequence we see that thefield at the interface has the widest spreading and has a single peak atthe center. As the depth increases, the field pattern gradually shrinksand deforms, and at the depth of 0.5 meters, the field begins to splitfrom one peak into two peaks. Thereafter, the field pattern continues toreduce in size and the two peaks separate further and further apart.This focusing process appears to end at a depth of about 0.85 meters andthen the change reverses. The field pattern starts to expand and the twopeaks again merge. The image sequence of the level field distributiondemonstrates the process of the field converging to the source, which isthe inverse process of the field spreading from the source.

[0067] By reconstructing the field and observing the change of the fieldimage with depth, it can be clearly seen that there are actually twoseparate sources located in the conductive medium, which could not berecognized from observing the field at the interface. The location ofthe sources can now be determined by finding the most confined fielddistribution pattern, or the focused field image. In this example, themost confined field image appears at the level plane which is 0.85meters from the interface. The position of the two bright spots in thefield image shows the location of the two dipoles in the x-y plane,which are (−0.25,0) and (0.25,0), respectively. The vertical location ofthe dipoles is given by the depth of the focused level plane, which isat z=−0.85 m.

[0068] Comparing the estimated source location with the true sourcelocation we see that the horizontal position of the two sources matchesexactly the true position but that the vertical position is 0.15 metersshallower than the true position. The errors in depth estimation maycome from several sources. The finite hologram aperture can causewraparound errors in the reconstructed field. The infinite spectral bandof the idealized dipole source results in an aliasing effect in samplingthe field from the continuous to the discrete. A more detaileddiscussion on the aliasing effect is given below, followed by anothersimulation with a bandlimited function of two discrete point sources forwhich the aliasing effect is effectively reduced. The resultant depthestimation through field reconstruction becomes much closer to the truedepth.

[0069] The dipoles' field at the surface is generated by the analyticformula given by Eqs. (11-12) and is a continuous function of horizontalcoordinates. The field reconstruction is accomplished by a discretenumerical processing of the continuous field function. According tosampling theory, if the Fourier transform h(t) is zero for allfrequencies greater than the Nyquist critical frequency f_(c), then thecontinuous function h(t) can be uniquely determined from a knowledge ofits samples taken at or exceeding 2f_(c). If a continuous function isnot bandlimited to less than the Nyquist critical frequency, thespectrum that lies outside of the frequency range (−f_(c), f_(c)) willbe folded over or aliased into the range. The dipole source used in thesimulation, mathematically, is an impulse function and has an infinitebandwidth. Therefore, when sampling this infinite bandwidth field atdiscrete values, it will always contain aliasing errors in the spectrum.In the field reconstruction process, the spectral components arepropagated backward from the interface to the level plane according toEq. (8). As indicated in that expression, even for a very small error,it will be exponentially amplified with the propagation distance.

[0070] The source localization simulation will now be repeated with abandlimited source function, but instead of computing the field at theinterface from Eqs. (11-12), the interface field is constructed in analternative way. The two point sources located at plane z=−1 m arerepresented by a two-dimensional discrete function

s(p,q)=δ(pΔ+0.25)δ(qΔ)+δ(pΔ−0.25)δ(qΔ), −128≦p,q≦127   (13)

[0071] where δ( ) is the Kronecker delta function defined as$\begin{matrix}{{\delta (n)} = \left\{ {\begin{matrix}{0,} & {n \neq 0} \\{1,} & {n = 0}\end{matrix},} \right.} & (14)\end{matrix}$

[0072] p and q are integer variables, and Δ is a spacing constant withthe value of 0.0625 m.

[0073] This function is Fourier transformed and propagated one meterforward to get it to the interface. Then it is inverse Fouriertransformed to obtain the field distribution at the interface. Thisresulting interface field has its values at discrete points spaced by0.0625 m and in a finite area of about 16 m×16 m. A hologram of thefield with a sampling interval of 0.25 m is formed from this interfacefield in an aperture from −4 m to 3.75 m in both dimensions, as shown inFIG. 5. In comparison with the field of ideal dipoles in FIG. 3, thisfield value drops at a slower rate when away from the center pointbecause it does not contain some high frequency components.

[0074]FIG. 6 displays the reconstructed field images at depths in arange of 0.7-1.1 m. It shows that the field image focused at the depthof 0.95 meter from the interface. The spectral bands are much morelimited for the field induced from real objects, and depth estimationerrors in some real cases are expected to be further reduced.

[0075] The numerical simulations demonstrate that, after applyingnearfield electromagnetic holography to process the detected surfacefield data, not only can closely placed sources be resolved even if theyare separated only by 5×10⁻⁴ of the wavelength, but their locations in3D-space can also be determined.

[0076] In practical application, the invention is used to localizeburied objects with an active EM source. An active electromagneticsource excites the object to radiate an electromagnetic field. Theobject field transmitted directly from the object is what is needed toobtain the location of the object.

[0077] Generally, for a system operating in an electromagnetic inductionmode, the signals detected at the receive coil are a mixture of theprimary field directly from the source and the secondary field comingfrom the object. The primary field is usually several orders ofmagnitude greater than the secondary field. It is usually very hard toseparate the secondary field from the primary one.

[0078] The commonly used method for frequency-domain electromagneticinduction measurements is to use bucking coils to cancel out the primaryfield at some point where the receiver coil is placed. For example, inthe rigid boom slingram method, the data is collected in such a way thatthe receiver coil is at a fixed distance with respect to the transmittercoil during the entire measurement. The cancellation of the primaryfield in this case needs to be done only at one particular point.

[0079] However, for the invention, the field at multiple locations needsto be measured relative to the transmitter coil. If the range betweenthe transmitter coil and the receiver coil varies, the primary fieldwould have to be bucked out at each receiver location with differentbucking coils. In order to effectively remove the primary source fieldfrom the detected field, the time-domain method is used for themeasurement of the object field.

[0080] The time domain system works in an on-and-off mode. During the onperiod, the transmitter coil current is turned on and an impulse fieldis generated. After a short duration the current in the transmitter coilis turned off for an interval of time. During the off period, thedetection coil measures the response from the object, effectivelypreventing the primary field from being measured together with thesecondary field.

[0081] Generally, after the source is turned off, the response includesboth the response from the earth as well as from objects of interest.The response from the earth decays faster than the response from themetallic objects. By waiting long enough one can virtually avoid theresponse from the earth, and only detect the decay tail of the responsefrom the object. The time response of the secondary field is thenFourier transformed to the frequency domain, and a field hologram of theobject at the detection plane is formed at a selected frequency and usedfor the field reconstruction.

[0082]FIG. 7 shows a simplified diagram of the time-domainelectromagnetic (TEM) technique. After a current loop transmitter isplaced in the vicinity of the buried target, a steady current is causedto flow in the transmitter loop for a sufficiently long time to allowturn-on transients in the ground to dissipate. The loop current is thenquickly turned off. According to Faraday's Law, the rapid reduction inthe transmitter's magnetic field induces an electromotive force (emf) innearby conductors. This emf causes eddy currents to flow in theconductor with a characteristic decay time that depends on theconductivity, size, and shape of the conductor. The decay currentsgenerate a secondary magnetic field, the time rate-of-change of which ismeasured by a receiver coil located above the ground.

[0083] As depicted in FIG. 8, an implementation of the TEM technique iscomposed of three major systems: a pneumatically-driven, mechanicalscanning frame for the receiver coils; the transmitter and receiverelectronics; and the data acquisition system.

[0084] The decaying magnetic field over the area above the target ismeasured by an array, linear or two-dimensional, of receiver coilslocated on a variable height coil cart which is moved on an X-Y frame,much like an “X-Y plotter”. The X-Y plotter frame can be constructed offiberglass and plastic. Both the coil cart and support frame can bepositioned using a pneumatically driven claw/piston system asillustrated in FIGS. 9-11.

[0085]FIG. 9 shows the claw portion of the claw/piston system with pegs12, 13, 14. The claw is attached to support plate 16 and pivots aboutaxle 18. Also attached to the axle is control arm 20; elastic means 22is attached to the end of the control arm opposite from the axle and topeg 13. Slotted brackets 24, 26 are attached respectively to thecarriage or cart to be moved and to the frame over which it is to bemoved with the support plate sliding back and forth inside the slots inthe slotted brackets.

[0086]FIG. 10 shows the claw attached to an air/hydraulic cylinder 28via a connecting rod 30 which attaches to the axle and to piston 32located in the air/hydraulic cylinder. The air/hydraulic cylinder canoperate in a push/pull fashion as the piston is cycled back and forthwith the piston thereby moving the support plate and claw in the samedirection.

[0087]FIG. 11(a) illustrates the claw/piston system attached to amoveable cart 34 on wheels 36 resting on the rail 38 of thescanning/support frame. FIG. 11(a) also illustrates the system at thebeginning of a pull stroke with the claw engaging a peg on the rail. Theair/hydraulic cylinder is attached to the wheeled cart. Air/hydraulicpressure in the cylinder then pushes the piston back causing the cart tobe pulled forward, as shown in FIG. 11(b). The piston is then extendedto move the claw to the next peg on the rail as shown in FIG. 11(c) withthe combination of the elastic means on the support arm and the slopededge on the claw allowing the claw to ride over the next peg. Once overthe rail peg, the claw slides a small distance ahead of it. The cartremains stationary during this operation. The operation then beginsagain with the air/hydraulic cylinder pulling the piston in and causingthe claw to engage the peg and pull the cart forward. An air compressorand pneumatic directional control valves are located away from theframe, near the data acquisition system.

[0088] A simplified block diagram of the TEM system is shown in FIG. 12and a diagram of the individual receiver amplifiers and generaltransmitter electronics is shown in FIG. 13. The receiver coilelectronics are located near the receiver coils and are connected to thedata acquisition system via a cable. The transmitter coil current iscontrolled by a 50% duty cycle, variable frequency quartz crystaloscillator operating at about 20 Hz. The oscillator's output isconnected to a solid state switch near the transmitter coil. Current tothe switch and transmitter coil is provided by a power supply located atthe data acquisition system.

[0089] By way of example, the transmitter coil can be 1 m by 1 m squareand constructed of two turns of wire wound around two-inch diameter PVCtubing. The coil is shunted with a resistor to improve its turn-offtime. As constructed, the transmitter coil and switch system can turnoff about 12 A in about 450 ns (90% to 10%) with little ringing. Currentin the transmitter coil is monitored via a series resistor connected onthe ground side of the power supply. The voltage drop across theresistor is measured by the data acquisition system.

[0090] By way of example, the toroidal receiver coils can be 20 cm indiameter and have 100 turns of wire. In this configuration, theirfrequency response (di/dt vs frequency) has been tested and found to belinear up to about 80 kHz. Each receiver coil is connected to its ownamplifier via a short cable.

[0091] The receiver coil amplifiers, plus a battery operated powersupply are housed in a water-resistant fiberglass enclosure. A receivercoil amplifier includes five components: input protection, analog switch(optional), instrumentation amplifier, operational amplifier and currentdriver.

[0092] The receiver coil input to the active circuitry is protected by afour diode/resistor array that clips any input signal at the positive ornegative power supply voltage level. This protection is needed since thereceiver coil can generate several hundred volts when it is near anactive, full power transmitter coil.

[0093] An optional analog switch can be used for extra protection and isdriven by a variable delay trigger that is synchronized with thetransmitter signal. The purpose of the analog switch is to connect thereceiver coils to the high gain amplifiers after the initial, highvoltage turn-off transient from the transmitter coil has decayed in thereceiver coil.

[0094] A low-noise, instrumentation amplifier provides the first stageof amplification. The gain of the instrumentation amplifier was set at100. The instrumentation amplifier is followed by a low-noise,operational amplifier configured as a two-pole, low pass active filterwith a gain of 100 and a 3 db point of about 20 kHz.

[0095] In order to drive the long data lines between the amplifier andthe data acquisition system, a current driver was placed inside thefeedback loop of the filter/amplifier. A 50 Ω decoupling resistorconnects the amplifier to the data line.

[0096] Data acquisition is provided by an Analogic 12-channel, 16-bitanalog-to-digital converter (ADC) subsystem installed in a Dynex 486, 33MHz IBM compatible personal computer. The Analogic card has 4 Megabytesof onboard RAM that allows the ADC to collect about 6 seconds ofuninterrupted data at 83 K samples/s. The data are stored on a Bernoullidisk drive for post-test data processing.

[0097] In a typical data collection scenario, the transmitter coil isplaced over a suspected target. Centering of the transmitter coil overthe target is not critical since the spatial magnetic field measurementswill localize the target in a XYZ coordinate system referenced to the XYscanning frame. The first data collection station is at one end of theXY scanning frame. The data acquisition system collects about 6 secondsof data on the ADC RAM board. It then transfers the data to a Bernoullidisk. While data are being transferred to the disk, the scanning framemoves the receiver coils to the next data collection station. Thissequence of operations is repeated until the scanning frame has sweptthe entire test area.

[0098] A preanalysis program separates the individual receiver channelsfrom a pack binary format created by the data collection program. Thedata channels are synchronized with the transmitter pulses and averagedfor about 100 transmitter pulse cycles. The resulting averaged timeseries is recorded as an ASCII text file. Alternatively, this averagingcan be done during data collection.

[0099] The analysis program is written in the IDL programming languageand performs the following steps. The spectrum of the magnetic field isobtained by applying an FFT to the individual data time series. At achosen frequency, the nearfield electromagnetic holography method isapplied to the data to reconstruct the spatial field distribution overthe horizontal plane at a specified depth. For each reconstructedmagnetic field distribution (RMFD) at a specified depth, the peak fieldis normalized to 1. By examining the RMFDs in the horizontal planes atvarious depths, the XYZ position of the target, relative to the scanningframe/receiver coils, can be determined. The location of the target isthe point where the peak in the RMFD is in “focus” or most well defined.The results discussed below will make this idea of “focus” clearer.

[0100] Measurements have been conducted with prearranged metallicobjects in preliminary tests using the PROTEM 57 sensor system fromGeonics Limited. The PROTEM 57 is a transient time domain system thatmeasures the time response of the time rate of change of the magneticfield. This system comes with a 5 m×5 m transmitter loop and a receivercoil of diameter about 60 cm. The 5 m×5 m transmitter loop was replacedwith a smaller transmitter coil of 1 m×1 m in the measurements.

[0101] Test objects included steel pipes and a cannon ball. The steelpipes were tested both in air and in the ground, and the cannon ball wasburied in the ground. The test configurations are shown in FIG. 14. Forthe above ground test, two identical steel pipes 40 cm long and 15 cm indiameter were fixed to a wooden bar and suspended about 1 meter off theground. The two pipes were separated by 1 meter from center to centerand oriented vertically, as shown in FIG. 14(a). The 1-meter transmittercoil was fixed on the ground below the pipes with its center slightlyoff the center line of the two pipes. The receiver coil was moved fromone measurement point to another with a spacing of one half meter. Themeasurements were made at the surface of the ground covering a 3 m×3 mgrid centered under the objects. The reconstructed magnetic field imagesat various heights are shown in FIG. 15.

[0102] The same pair of steel pipes were also tested when buried in theground. The pipes were buried at 40 cm from the surface to the top witha separation of 1 meter, and the 1-meter transmitter coil was at thesurface directly above the pipes, as shown in FIG. 14(b). Themeasurement went through a quadrant of the grid with spacing of 0.5 m.Data for the rest of the full grid were obtained by a mirror-reflectingoperation over the measured one-quadrant data, as the center of thetransmitter coil had been carefully adjusted to be on the symmetry lineof the two pipes. The reconstructed images for the buried steel pipesare shown in FIG. 16 and plots of the reconstructed magnetic fielddistribution at four depths are shown in FIG. 17.

[0103] In the case of two steel pipes suspended above the ground, theat-surface field image in FIG. 15 shows a big spot which looks likethere is only one object detected and with unknown height. But, as theheight increases, the spot in the field image shrinks, deforms, andsplits from one into two at the height of 0.3 m. It is noticed, from thefield images in FIG. 15, that the separation of the two spots in theimages from 0.7 m to 1.0 m is very clear, and the gaps between the twospots are prominently wider. This feature reflects the pipes' verticallocation which occupied from 0.62 m to 1.02 m. Furthermore, the spots'positions in these images match the pipes' horizontal locations as well.The uneven strength of the two spots of the field image is probably dueto the off-center placement of the transmitter coil.

[0104] The reconstructed field images in FIG. 15 for the buried pipespresent a clear picture of the resolving and merging process of theindividual field of the two pipes even though a half-overlapped field isseen at the surface. The phenomenon of prominent separation of the twospots for quite a long range is also shown in this example. It occurredin the images from 0.4 m to 0.7 m. In comparison, the depths from 0.4 mto 0.8 m are where the pipes were actually located. The image patternchange within those depths is much slower compared with the changewithin other depths of the same distance above or below the pipes.Apparently, the field was concentrated to the pipes in those depthswhere the pipes were located, and quickly spread away at other depths.

[0105] In FIG. 17, Plot A is the reconstructed magnetic fielddistribution (RMFD) at the plane of the receiver coil. The two steelpipes project a very strong magnetic signal at the surface which appearas a large peak with two smaller peaks on top. Plot B, RMFD depth equalto 20 cm, shows the two smaller peaks separating indicating that thelarge peak in Plot A was in fact caused by two separate targets. The twotargets are coming into “focus” as their true depth is approached. At anRMFD depth equal to 60 cm, plot C shows the two peaks clearly separated.RMFDs at depths between 40 cm and 70 cm are almost identical, with welldefined peaks. This is the region occupied by the pipes. However, asshown in plot D, at a RMFD depth equal to 100 cm, the peaks have startedto recombine, and become less distinct. This depth is beyond the bottomof the pipes, the RMFD becomes “defocused.”

[0106] The ability of the holographic technique of the invention toresolve horizontal position is also shown in FIG. 17. The two peaks ofthe RMFD at 60 cm depth are 1 m apart. This inferred separation distancematches exactly the 1 m separation of the buried pipes.

[0107] In the same preliminary test, a cannon ball of 20 cm in diameterwas buried at a depth of 60 cm, as shown in FIG. 14(c). The transmittercoil was fixed at the surface directly above the ball, and the receivercoil was moved at a spacing of 0.5 m for a 4 m×4 m grid of points. FIG.18 shows the reconstructed images of the cannon ball.

[0108] The buried cannon ball test demonstrates how a single object maybe located through the field image observation. For a single object, themain goal is to determine the buried depth, because the horizontalposition can be readily identified from the measured field distribution.Observing the images in FIG. 18 from converging to diverging shows thatthe focused image is at a depth of about 0.5 meters, while the ball wasactually located with its top at 0.5 m and its center at 0.6 m.

[0109] Follow on field tests utilized the TEM system depicted in FIG. 8and two small aluminum (Al: 6061-T6) disks, 12.7 cm in diameter and 5.7cm thick, as test objects. To facilitate different testingconfigurations, the disks were not buried but were placed on thesurface, in the center of the transmitter coil. The disks were separatedby 51 cm and the receiver coil array was raised to 41 cm above thecenter of the disks. To speed up the data collection, only two thirds ofthe test area was scanned as the magnetic field was assumed to besymmetric about the centerline between the two disks. The missing datapoints in the unscanned area were filled in by the data points in thescanned area.

[0110]FIG. 19 shows plots of RMFDs at four depths. Plot A is the RMFD atthe plane of the receiver coils. Because the two aluminum disks projecta weak magnetic signal, one cannot be certain as to what kind of targetis being scanned. At a RMFD depth equal to 20 cm, plot B shows two peaksbeginning to appear. At a RMFD depth equal to 40 cm (approximate targetdepth), plot C clearly shows the two peaks separated. In plot D, RMFDwith a depth equal to 55 cm, the peaks start to recombine, and becomemore diffuse, and out of focus.

[0111] The two peaks in FIG. 19 indicate that the horizontal separationof the aluminum targets is about 60 cm (three grid points). The realseparation distance was 51 cm.

[0112] The receiver coil signal is approximately proportional to thethird power of the range to the target. Small range changes cause largechanges in received signal strength. FIG. 19 shows that the RMFD peaksare not symmetric in amplitude. This is because the receiver coil arraywas not precisely aligned with the targets as the scanning frame movedacross the test area. In this case, as the receiver coil array wasscanned over the two targets, the receiver coils were closer to the‘right’ target (as shown in FIG. 19) than to the ‘left’ target. Hence,the signal was stronger when the receiver coils were over the ‘right’target. However, signal amplitude is not the important parameter in theTEM holographic technique. It is the spatial properties that areimportant.

[0113] Through the above field tests, it has been demonstrated thatmultiple objects located as close to each other as 1 meter, which 10⁻³of the wavelength of the EM wave, can be resolved and individuallylocalized with fairly good accuracy by reconstructing the field imagesat level planes using the nearfield holographic method. The positionalresolution for buried metal objects in the XY plane is on the order ofthe receiver coil measurement spacing while the resolution in the Zdirection depends on the data scanning window, receiver coil spacing aswell as the dynamic range of the sensor system. The tests also show thatthe time-domain electromagnetic system for data acquisition is suitablefor measuring the object field for the field image reconstruction in thenearfield holography method.

[0114] The numerical computations involved in the field reconstructionprocess is mainly that of obtaining the Fourier transforms. With theavailable Fast Fourier Transform (FFT) algorithm, computation isrelatively fast and a real-time localization system is achievable.

[0115] A new underground object localization method—nearfieldelectromagnetic holographic imaging method has been developed. Itlocalizes underground objects through field image reconstruction byutilizing spatial information of the field measured at the surface ofthe ground with a low frequency electromagnetic field. Both numericalsimulation and field tests have shown that with this method buriedmetallic objects can be localized with fairly good accuracy. It has beenshown that closely spaced multiple objects can be individually localizedwith this method even in the case that their resultant fields at thedetection plane show only a single peak.

[0116] Unlike the conventional holographic method in which theresolution is limited to the order of a wavelength, the nearfieldholographic method utilizes the evanescent waves in field reconstructionleading to a resolution almost independent of the wavelength. Alocalization resolution of about 5×10⁻⁴ of a wavelength has beenobtained in a simulation, and a resolution of 10⁻³ of a wavelength hasbeen found in a field test.

[0117] A preliminary field test demonstrates that with the transienttime domain data acquisition method for measuring the object field, thedifficulty of separating the induced object field from the primarysource field encountered in electromagnetic induction measurements canbe overcome. With the combination of the nearfield holography method andthe available FFT algorithm a real time system for underground objectlocalization is achievable.

We claim:
 1. A method for locating a buried, metallic object comprisingthe steps of: placing a current loop transmitter in the vicinity of theburied object; turning on the transmitter to cause a steady current toflow in the transmitter loop for a sufficiently long time to allowturn-on transients in the ground to dissipate; quickly turning off theloop current; and using an above ground receiver coil to measure thetime rate-of-change of a secondary field generated by eddy currentsflowing in the object produced by an electromotive force induced by therapid reduction in the transmitter's field.
 2. An apparatus for locatinga buried, metallic object comprising: a transmitter coil; a plurality ofreceiver coils; means for moving the receiver coils over the area abovethe object; and means for acquiring and processing data.
 3. Theapparatus as recited in claim 2, the moving means comprising: means forsupporting the receiver coils in an array and allowing vertical andhorizontal movement of the array; and means for positioning the array.4. The apparatus as recited in claim 3, the positioning meanscomprising: a piston and claw means; pneumatic directional controlvalves for driving the piston and claw means; and an air compressor. 5.The apparatus as recited in claim 4, further comprising: an oscillatorfor controlling the transmitter coil; and a solid state switch connectedto the oscillator for turning the transmitter coil on and off.
 6. Theapparatus as recited in claim 5, further comprising a power supply. 7.The apparatus as recited in claim 5, the transmitter coil furthercomprising: a resistor for shunting the coil to improve the turn-offtime of the coil; and a series resistor connected on the ground side ofa power supply for monitoring the current in the coil.
 8. The apparatusas recited in claim 5, further comprising a plurality of amplifiers,each amplifier connected to a receiver coil.
 9. The apparatus as recitedin claim 8, the amplifier further comprising: means for protecting theactive circuitry from the receiver coil input; an analog switch; aninstrumentation amplifier; an operational amplifier; and a currentdriver.
 10. The apparatus as recited in claim 9, the protecting meanscomprising a diode/resistor array for clipping any input signal at thepositive or negative power supply voltage level.
 11. The apparatus asrecited in claim 4, the piston and claw means comprising: a claw forengaging a first peg on the supporting means; a piston for pulling theclaw when engaging the first peg to move the supporting means and forpushing the claw to disengage the claw from the first peg and move theclaw to a second peg.